Question

A realtor in Oregon found that the selling price (in thousand dollars) of the house and the age of the house (how long since it was built) was highly correlated (r=–0.6). She collected some data and derived the following regression model.

Y = 260 – 2.5X

(1) Given above information, what would be the expected selling price for a house that was build 20 years ago?

(2) If another house is 8 years newer than the one mentioned in (1), will be the selling price higher or lower, and by how much?

Select one:

a. (1) 210 thousand dollars; (2) 8 thousand dollars lower.

b. (1) 210 thousand dollars; (2) 8 thousand dollars higher.

c. (1) 310 thousand dollars; (2) 12 thousand dollars higher.

d. (1) 240 thousand dollars; (2) 20 thousand dollars lower.

e. (1) 210 thousand dollars; (2) 20 thousand dollars higher.

Answer 1

Solution: Correlation refers to the degree of relation between two variables.

A zero correlation between two variables means that they are not related and any change in the value of one variable will not impact the other variable's value.

A negative correlation represents an indirect relation between the two variables and a Positive correlation shows that the two variables move in the same direction.

Because there is a negative correlation between the price and age of the house, it means that the older the house, the lesser will be its selling price and vice versa.

Regression is used to estimate the value of a dependent variable using the change in the independent variable with the help of Regression equations.

We are given a Regression equation that is as follows :

Y = 260-2.5X, where Y = Selling price of the house and X = Age (in years ) of the house

The above model is derived on the basis of the value of correlation which is -0.6.

The negative sign with X indicates the negative relation between the Selling price and Age of the house and hence, variables Y and X are denoted accordingly.

a) Using the above model and the age of the house as equal to 20 years,

Y = 260-2.5*20 = 260 - 50 = 210 thousand dollars

b) If the age of the house is 8 years less, it means use X= 20-8 =12 and,

Y = 260-2.5*12 = 260 - 30 = 230 thousand dollars

It means that the selling price of the newer house will be 20 thousand dollars (230-210) higher.

Conclusion: Based on the above calculations, the correct answer is Option E

All the other options are incorrect because of the calculations made above.